{"paper":{"title":"Isometric embedding of $\\ell_1$ into Lipschitz-free spaces and $\\ell_\\infty$ into their duals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marek C\\'uth, Michal Johanis","submitted_at":"2016-04-14T12:21:55Z","abstract_excerpt":"We show that the dual of every infinite-dimensional Lipschitz-free Banach space contains an isometric copy of $\\ell_\\infty$ and that it is often the case that a Lipschitz-free Banach space contains a $1$-complemented subspace isometric to $\\ell_1$. Even though we do not know whether the latter is true for every infinite-dimensional Lipschitz-free Banach space, we show that the space is never rotund.\n  Further, in the last section we survey the relations between \"isometric embedding of~$\\ell_\\infty$ into the dual\" and \"containing as good copy of~$\\ell_1$ as possible\" in a general Banach space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.04131","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}